Baryogenesis through Leptogenesis Mu-Chun Chen, University of California at Irvine Giada Carminati for WPA Workshop on Search of New physics with Leptons, UNAM, October 17, 2018
Evidence of Matter-Antimatter Asymmetry • CMB anisotropy ∆ T � = a lm Y lm ( θ , φ ) | a lm | 2 � � C l = T l,m • Big Bang Nucleosynthesis • primordial deuterium abundance ⟺ agree with WMAP • 4 He & 7 Li ⟺ discrepancies • WMAP + Deuterium Abundance n B ≡ η B = (6 . 1 ± 0 . 3) × 10 − 10 n γ 2 Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions rs Universe Now Early Universe [Picture credit: H. Murayama] • Baryon number can be generated dynamically, if • violation of baryon number • violation of Charge (C) and Charge Parity (CP) • departure from thermal equilibrium 3 Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Baryon Number Asymmetry beyond SM • Within the SM: ‣ CP violation in quark sector not su ffi cient to explain the observed matter- antimatter asymmetry of the Universe ‣ accidental symmetries L e , L μ , L τ , total L ‣ massless neutrinos, no cLFV • neutrino oscillation ⇒ non-zero neutrino masses • physics beyond the Standard Model • new CP phases in the neutrino sector • neutrino masses open up a new possibility for baryogenesis Fukugita, Yanagida, 1986 Leptogenesis 4 Mu-Chun Chen, UC Irvine Leptogenesis and Neutrino Masses
Plans • Theoretical Foundation of Baryogenesis: • Sakharav’s Three Conditions • Mechanisms for Baryogenesis & Their Problems • Sources of CP violation • Standard Leptogenesis (“Majorana” Leptogenesis) • Dirac Leptogenesis • Gravitino Problem • Non-standard Scenarios • Resonant Leptogenesis • Soft Leptogenesis • Non-thermal Leptogenesis • Connection between leptogenesis & low energy CP violation Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
References • W. Büchmuller, hep-ph/0502169 • A. Riotto, hep-ph/9901362 • M. Trodden, hep-ph/0411301 • “TASI 2006 Lectures on Leptogenesis,” M.-C. Chen, hep- ph/0703087 Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions Baryon Number Violation • necessary for baryon symmetric Universe (B=0) → Universe with B ≠ 0 • GUT theories: • quarks and leptons in same representations → B-violation naturally through interactions with gauge or scalar fields • SM: • B & L accidental symmetries • preserved at tree level • t’Hooft: non-perturbative instanton e ff ects (B+L) ≠ 0, (B-L) = 0 Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions • Classically: B & L conserved • At quantum level, non-vanishing ABJ triangular anomaly through interactions with EW gauge fields � B µ ν � L = N f µ ν � W pµ ν − g � 2 B µ ν � ∂ µ J µ B = ∂ µ J µ g 2 W p 32 π 2 ⇒ (B+L) is violated • vacuum structure of non-abelian gauge theories: • changes in B & L ↔ changes in topological charges s, ∆ B = ∆ L = N f ∆ N cs = ± 3 n , � O B + L = ( q L i q L i q L i � L i ) , i =1 , 2 , 3 Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions • 12 fermion Processes, e.g. u + d + c → d + 2 s + 2 b + t + ν e + ν µ + ν τ • T=0: transition rate negligible Kuzmin, Rubakov, Shaposhnikov y, Γ ∼ e − S int = e − 4 π / α = O (10 − 165 ) • In thermal bath: transition by thermal fluctuations • at T > height of barrier: no Boltzmann suppression = k M 7 Γ B + L • T < T ew : ( α T ) 3 e − β E ph ( T ) ∼ e − MW E sp ( T ) � 8 π W g � H ( T ) � α kT V ≥ • T > T ew : Γ B + L ∼ α 5 ln α − 1 T 4 ⇒ B-violating process V unsuppressed • Sphelaron process in thermal eq. T EW ∼ 100 GeV < T < T sph ∼ 10 12 GeV Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions C and CP Violations process branching fraction ∆ B • superheavy X boson decay 2/3 X → qq α 1 − α -1/3 X → q � -2/3 X → qq α • Baryon number produced 1 − α 1/3 X → q � � 2 � � � − 1 = α − 1 B X = α + (1 − α ) 3 , 3 3 � � � 1 � � � − 2 α − 1 B X = α + (1 − α ) = − , 3 3 3 • net Baryon number � ≡ B X + B X = ( α − α ) • if CP is conserved: d, α = α , r, � = 0. • Toy Model: two heavy scalar fields: X, Y; 4 fermions f i L = g 1 Xf † 2 f 1 + g 2 Xf † 4 f 3 + g 3 Y f † 1 f 3 + g 4 Y f † 2 f 4 + h.c. • possible decays X → f 1 + f 2 , f 3 + f 4 , Y → f 3 + f 1 , f 4 + f 2 , Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions f 3 f 4 f 3 • at tree level: f 1 Y Y X X g 3 g 4 g 1 g 2 → Γ ( X → f 1 + f 2 ) = | g 1 | 2 I X f 2 f 1 f 2 f 4 → 1 | 2 I X Γ ( X → f 1 + f 2 ) = | g ∗ phase space factor equal s I X and I X ⇒ no asymmetry • at one-loop ∗ g 3 ∗ g 3 g 2 g 2 f 3 f 1 f 3 f 4 f 3 f 1 f 3 f 4 X X Y Y g 2 g 1 g 4 g 3 Y Y X X f 4 f 2 f 2 f 1 f 2 f 1 f 2 f 4 ∗ ∗ g 4 g 1 g 1 g 4 → → I XY : phase space + kinematics Γ ( X → f 1 + f 2 ) = g 1 g ∗ 4 I XY + c.c. 2 g 3 g ∗ Γ ( X → f 1 + f 2 ) = g ∗ 1 g 2 g ∗ 3 g 4 I XY + c.c. Γ ( X → f 1 + f 2 ) − Γ ( X → f 1 + f 2 ) = 4 Im ( I XY ) Im ( g ∗ 1 g 2 g ∗ 3 g 4 ) → Γ ( X → f 3 + f 4 ) − Γ ( X → f 3 + f 4 ) = − 4 Im ( I XY ) Im ( g ∗ 1 g 2 g ∗ 3 g 4 ) Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions • total asymmetry � X = ( B 1 − B 2 ) ∆Γ ( X → f 1 + f 2 ) + ( B 4 − B 3 ) ∆Γ ( X → f 3 + f 4 ) Γ X ( 4 Im ( I XY ) Im ( g ∗ 1 g 2 g ∗ � X = 3 g 4 )[( B 4 − B 3 ) − ( B 2 − B 1 )] Γ X 4 Im ( I � XY ) Im ( g ∗ 1 g 2 g ∗ � Y = 3 g 4 )[( B 2 − B 4 ) − ( B 1 − B 3 )] Γ Y • non-zero total asymmetry ε = ε X + ε Y • two B-violating bosons with masses > sum of loop fermion masses • complex coupling constants: CP violation from interference between tree and 1-loop diagrams • non-degenerate X and Y masses Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions Departure from Thermal Equilibrium • B: odd under C and CP • in equilibrium: < B > T = Tr[ e − β H B ] = Tr[( CPT )( CPT ) − 1 e − β H B )] = Tr[ e − β H ( CPT ) − 1 B ( CPT )] = − Tr[ e − β H B ] ⇒ average <B> T = 0 • Possible ways to achieve departure from thermal equilibrium • out-of-equilibrium decay of heavy particles: • GUT baryogenesis, leptogenesis • EW phase transition: EW baryogenesis Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
Three Sakharov Conditions • Leptogenesis: Out-of-equilibrium decay of heavy particles • superheavy particle X: decay rate Γ X , Mass M X • at T ~ M X : become non-relativistic • if Γ X < H: • X cannot decay on the time scale of the expansion xpansion. The X particles will then rem • remains thermal abundance e, n X = n X ∼ n γ ∼ T 3 , for T � M X . • at T > M X : interact so weakly, cannot catch up expansion • decouple from thermal bath while relativistic • populate at T ~ M X with abundance >> than in equilibrium • recall: in equilibrium n X = n X � n γ for T � M X , n X = n X � ( M X T ) 3 / 2 e − M X /T � n γ for T � M X Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis
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